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It looks like you're using the older, free version, where some things are different. But I can make some pretty good guesses. I'd appreciate if people corrected anything I said that was wrong.

The number after the "->" should be the weapon's maximum penetration value. Unless your stats are really good, your effective penetration value should be less than this. Your effective penetration value will still be better for weapons with higher penetration. Higher penetration values means it's more likely for you to get past an enemy's armor. If you don't get past their armor, no damage is done to them and you see a closed circle shape on them (circle with a hole in it means they dodged).

The numbers of the form #d# after the heart symbol determine how much damage is done if you get past an enemy's armor (and they don't dodge your attack). The game takes the second of the two numbers, and rolls a random value from 1 to that number. So if the weapon was 2d5, then it would roll a random value from 1 to 5. The number before the d tells you how many times you roll a number like this. So if your weapon was 2d5 you'd roll a number from 1 to 5, and then another number from 1 to 5, and add them together. This makes some weird effects like how a 2d2 weapon always deals at least 2 damage but a 1d4 weapon might deal 1, and yet they have the same maximum damage. But it shouldn't make enough difference between the two to matter so much.

Generally speaking, there is no 'best' weapon type. If you're fighting an enemy with high av (armor value), then axes or cudgels are the way to go. If the enemy has low av, then longswords and the like are a better choice. But there are other ways to deal with high av enemies, like weapons with flaming, freezing, or electric, whose elemental damage ignores av. There are more, but I'll let you discover those on your own. I generally prefer axes in the early game, since they're good enough to pierce eyeless crab armor but still deal good damage, and since they're not hard to find usually. But if the store has a carbide longsword at the start, I won't turn it down just because it isn't an axe.

Lurker seems to have covered most of the basics of penetration and damage. Be aware that for ever 3 extra penetrations vs the opponents armour, you multiply your damage. This can lead to pretty large damage values against low armour targets. Additionally, you roll a dice before the Pen bonus (+7 for the club, for instance, if you have enough STR), which means some armoured oponents could "block" some of your attacks, but be damaged by others.

These Pen bonuses are dependent on the quality of your weapon, and your STR. Clubs have +2 to pen, Axes +1, swords and short blades +0. Swords can lunge for +2, though, and Axes can cleave through enemies armour, reducing it to a max of -4. Every tier, too, changes the maximum value your STR can help with penetration. Currently, you have a +5 to daggers (through STR or a certain DEX skill), which is why Iron and Bronze have the same PV value, even though Iron daggers max out at 6.

Ultimately, higher tier weapons are best because they have more damage dice, 2d6 vs 1d2, for example, and a higher maximum PEN, which helps you deal damage to armoured targets more effectively.

Hope this helps!

Oh, and you might be able to see the weapon max pen bonuses by going into options->User Interface -> Displayed Detailed Weapon Pen and Damage in Name